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Corresponding Author

Marwa A. Abd Elwahaab

ORCID

Esraa : 0009-0002-6153-5888 ;Abed: 0000-0001-7704-3146; Marwa: 0000-0003-0396-9979:

Subject Area

Mathematics and Engineering Physics

Article Type

Original Study

Abstract

Similarity/dissimilarity studies follow alignment-based or alignment-free methods. Many alignment-free methods involve selecting physicochemical properties. Most previous articles don’t explain their criteria for choosing the properties used. These heuristic approaches have, by definition, undeterministic and unreliable performance. Hence, there is a need for a powerful proxy for similarity/dissimilarity by a deterministic, reliable approach.

In this study, a physicochemical property is selected by a multi-criteria sequential selection process. The amino acids composing any protein sequence are replaced with their values of the chosen property to produce a discrete signal in the time domain.  The one-dimensional discrete Hadamard transforms our signal from the time to the frequency domain. The one-dimensional Discrete Hadamard transformation is well matched with the naturally quantized (i.e., integer) selected property. The Two-dimensional Hadamard transformation is also introduced, based on the common adjacency matrix. Two different protein descriptors are introduced for 1D and 2D Hadamard transformation-based approaches. Our approaches were applied to four sets of different lengths: 9 ND5, 8 ND6, 10 ACE2, and 33 spike protein sequences. Similarity/ dissimilarity matrices were calculated. Phylogenetic trees were created to prove the utility of our approaches. Our results from the two proposed approaches are compatible with evolutionary relationships. However, we recommend our approach based on the (1D) discrete Hadamard transformation, which is simpler, efficient, deterministic, and reliable. The computational order of the 1D Hadamard transformation is O (N logN), while the 2D Hadamard transformation is O (N^2).

Keywords

Similarity/dissimilarity analysis – Free alignment methods – AAindex1 indices’ multi-criteria sequential selection process – Hadamard Transformations – Correlation and significance analysis.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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